document.write( "Question 6763: I need help solving this word problem:\r
\n" ); document.write( "\n" ); document.write( "The sum of two numbers is 10. Their product is -24. Find the numbers. Write a complete solution \n" ); document.write( "

Algebra.Com's Answer #3726 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Try this!\r
\n" ); document.write( "\n" ); document.write( "Let the two numbers be x and y.
\n" ); document.write( "Then:
\n" ); document.write( " x + y = 10 Rewrite as: x = 10 - y and substitute into equation below.
\n" ); document.write( "xy = -24.\r
\n" ); document.write( "\n" ); document.write( "(10 - y)Y = -24 Solve for y.
\n" ); document.write( "10y - y^2 = -24 Add 24 to both sides and put into standard form.
\n" ); document.write( "y^2 - 10y - 24 = 0 Solve the quadratic by factoring.
\n" ); document.write( "(y + 2)(y - 12) = 0 Apply the zero product principle.\r
\n" ); document.write( "\n" ); document.write( "y + 2 = 0, y = -2
\n" ); document.write( "y - 12 = 0, y = 12\r
\n" ); document.write( "\n" ); document.write( "Now substitute these values of y into the original equations:\r
\n" ); document.write( "\n" ); document.write( "x = 10 - y
\n" ); document.write( "x = 10 - (-2)
\n" ); document.write( "x = 12\r
\n" ); document.write( "\n" ); document.write( "And:\r
\n" ); document.write( "\n" ); document.write( "x = 10 -y
\n" ); document.write( "x = 10 - 12
\n" ); document.write( "x = -2\r
\n" ); document.write( "\n" ); document.write( "The two numbers are: -2 and 12\r
\n" ); document.write( "\n" ); document.write( "Check:\r
\n" ); document.write( "\n" ); document.write( "12 + (-2) = 10, and
\n" ); document.write( "12(-2) = -24\r
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